Gravity-driven motion of a deformable drop or bubble near an inclined plane at low Reynolds number

The creeping motion of a three-dimensional deformable drop or bubble in the vicinity of an inclined wall is investigated by dynamical simulations using a boundary-integral method. We examine the transient and steady velocities, shapes, and positions of a freely-suspended, non-wetting drop moving due to gravity as a function of the drop-to-medium viscosity ratio, λ, the wall inclination angle from horizontal, θ, and Bond number, B, the latter which gives the relative magnitude of the buoyancy to capillary forces. For fixed λ and θ, drops and bubbles show increasingly pronounced deformation in steady motion with increasing Bond number, and a continued elongation and the possible onset of breakup are observed for sufficiently large Bond numbers. Unexpectedly, viscous drops maintain smaller separations and deform more than bubbles in steady motion at fixed Bond number over a large range of inclination angles. The steady velocities of drops (made dimensionless by the settling velocity of an isolated spherical drop) increase with increasing Bond number for intermediate-to-large inclination angles (i.e. 45° ⩽ θ ⩽ 75°). However, the steady drop velocity is not always an increasing function of Bond number for viscous drops at smaller inclination angles.